Solve the problem.
-A piece of cardboard is twice as long as it is wide. It is to be made into a box with an open top by cutting $3 \mathrm {~cm}$ squares from each corner and folding up the sides. Let $x$ represent the width of the original piece of cardboard. Determine a function $\mathrm { V }$ that represents the volume of the box in terms of $x$.
A) $V ( x ) = 6 x ^ { 2 }$
B) $V ( x ) = 3 x ^ { 2 } - 36 x + 108$
C) $V ( x ) = 6 x ^ { 2 } - 27 x + 27$
D) $V ( x ) = 6 x ^ { 2 } - 54 x + 108$

Question

Quizplus · Accepted Answer

The volume of the box, $V$, can be found by multiplying its length, width, and height. After cutting out the squares, the new dimensions are: width = $x - 2(3) = x - 6$, length = $2x - 2(3) = 2x - 6$, and height = $3$. Thus, $V(x) = (x - 6)(2x - 6)(3) = 6x^2 - 54x + 108$.

Solve the Problem 3 cm3 \mathrm {~cm}3 cm Squares from Each Corner and Folding Up the Sides

Solve the Problem $3 \mathrm {~cm}$ Squares from Each Corner and Folding Up the Sides